Triple solutions for nonlinear singular m-point boundary value problem

Volume 4, Issue 4, pp 262--269 http://dx.doi.org/10.22436/jnsa.004.04.04

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Authors

Fuli Wang - School of Mathematics and Physics, Changzhou University, Changzhou, China.

Abstract

In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem \[ \begin{cases} u''(t) + \beta^2u(t) = h(t)f(t, u(t)),\,\,\,\,\, 0 < t < 1,\\ u'(0) = 0, u(1) =\Sigma^{m-2}_{i=1}\alpha_i u(\eta_i), \end{cases} \] where \(0<\beta<\frac{\pi}{2}, f\in C([0,1]\times \mathbb{R}^+, \mathbb{R}^+). h(t)\) is allowed to be singular at \(t = 0\) and \(t = 1\). The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.

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Keywords

• m-point boundary value problem
• Positive solutions
• Fixed point theorem.

MSC

•  34B15
•  34B25

References

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